Can someone please help me with the following questions?

Question

1:Suppose you were given an ancient wooden box. If you analyze the box for carbon-14 activity and find that it is 50% of that of a new piece of wood of the same size, how old is the wood in the box?

2:How old is an Egyptian scroll made of papyrus that contains 75% of the amount of C-14 that would be found in a piece of paper today?

Please and thank you!

1. The half-life of a material is the time it takes for 1/2 of the material to disintegrate. Thus, the box, if it has lost 50% of its activity, must have gone through one half-life. What is the half-life of C-14? Take 1/2 of that.

2. Suppose you start with 100 atoms of C-14. If the activity is now 75%, we must have 75 atoms today.
ln(No/N)=kt
No=100
N=75
k=0.693/t_1/2
Substitute the half-life for t_1/2 to find k, then substitute k into the ln equation and solve for t.
Post your work if you get stuck and need further assistance.

1) The half-life of C-14 is 5730, so would the answer be 2865 years?

2)Is this how I should do it?
In(100/75)=.693/t1/2
But how do I do it when you said it's k*t and .693/t1/2 is .693 divided by t

2865 years is right.

For #2.
k= 0.693/5730 = ?? (plug in below).

ln(100/75)=k*t =
ln(100/75)=??*t
Solve for t.

Answer 1

ln(100/75)=0.00012185*t
t=ln(100/75)/0.00012185
t=5730 years